3,016 research outputs found
Gravity: A New Holographic Perspective
A general paradigm for describing classical (and semiclassical) gravity is
presented. This approach brings to the centre-stage a holographic relationship
between the bulk and surface terms in a general class of action functionals and
provides a deeper insight into several aspects of classical gravity which have
no explanation in the conventional approach. After highlighting a series of
unresolved issues in the conventional approach to gravity, I show that (i)
principle of equivalence, (ii) general covariance and (iii)a reasonable
condition on the variation of the action functional, suggest a generic
Lagrangian for semiclassical gravity of the form with
. The expansion of in terms of the
derivatives of the metric tensor determines the structure of the theory
uniquely. The zeroth order term gives the Einstein-Hilbert action and the first
order correction is given by the Gauss-Bonnet action. Any such Lagrangian can
be decomposed into a surface and bulk terms which are related holographically.
The equations of motion can be obtained purely from a surface term in the
gravity sector. Hence the field equations are invariant under the
transformation and gravity does not
respond to the changes in the bulk vacuum energy density. The cosmological
constant arises as an integration constant in this approach. The implications
are discussed.Comment: Plenary talk at the International Conference on Einstein's Legacy in
the New Millennium, December 15 - 22, 2005, Puri, India; to appear in the
Proceedings to be published in IJMPD; 16 pages; no figure
Why Does Gravity Ignore the Vacuum Energy?
The equations of motion for matter fields are invariant under the shift of
the matter lagrangian by a constant. Such a shift changes the energy momentum
tensor of matter by T^a_b --> T^a_b +\rho \delta^a_b. In the conventional
approach, gravity breaks this symmetry and the gravitational field equations
are not invariant under such a shift of the energy momentum tensor. I argue
that until this symmetry is restored, one cannot obtain a satisfactory solution
to the cosmological constant problem. I describe an alternative perspective to
gravity in which the gravitational field equations are [G_{ab} -\kappa T_{ab}]
n^an^b =0 for all null vectors n^a. This is obviously invariant under the
change T^a_b --> T^a_b +\rho \delta^a_b and restores the symmetry under
shifting the matter lagrangian by a constant. These equations are equivalent to
G_{ab} = \kappa T_{ab} + Cg_{ab} where C is now an integration constant so that
the role of the cosmological constant is very different in this approach. The
cosmological constant now arises as an integration constant, somewhat like the
mass M in the Schwarzschild metric, the value of which can be chosen depending
on the physical context. These equations can be obtained from a variational
principle which uses the null surfaces of spacetime as local Rindler horizons
and can be given a thermodynamic interpretation. This approach turns out to be
quite general and can encompass even the higher order corrections to Einstein's
gravity and suggests a principle to determine the form of these corrections in
a systematic manner.Comment: Invited Contribution to the IJMPD Special Issue on Dark Matter and
Dark Energy edited by D.Ahluwalia and D. Grumiller. Appendix clarifies
several conceptual and pedgogical aspects of surface term in Hilbert action;
ver.2: references and some clarifications adde
Scalar Field Dark Energy Perturbations and their Scale Dependence
We estimate the amplitude of perturbation in dark energy at different length
scales for a quintessence model with an exponential potential. It is shown that
on length scales much smaller than hubble radius, perturbation in dark energy
is negligible in comparison to that in in dark matter. However, on scales
comparable to the hubble radius () the
perturbation in dark energy in general cannot be neglected. As compared to the
CDM model, large scale matter power spectrum is suppressed in a
generic quintessence dark energy model. We show that on scales , this suppression is primarily due to different background
evolution compared to CDM model. However, on much larger scales
perturbation in dark energy can effect matter power spectrum significantly.
Hence this analysis can act as a discriminator between CDM model and
other generic dark energy models with .Comment: 12 pages, 13 figures, added new section, accepted for publication in
Phys. Rev.
The hypothesis of path integral duality II: corrections to quantum field theoretic results
In the path integral expression for a Feynman propagator of a spinless
particle of mass , the path integral amplitude for a path of proper length
connecting events and in a spacetime
described by the metric tensor is . In a recent paper, assuming the path integral amplitude to be
invariant under the duality transformation ,
Padmanabhan has evaluated the modified Feynman propagator in an arbitrary
curved spacetime. He finds that the essential feature of this `principle of
path integral duality' is that the Euclidean proper distance
between two infinitesimally separated spacetime events is replaced by . In other words, under the duality principle the spacetime
behaves as though it has a `zero-point length' , a feature that is
expected to arise in a quantum theory of gravity. In the Schwinger's proper
time description of the Feynman propagator, the weightage factor for a path
with a proper time is . Invoking Padmanabhan's `principle of
path integral duality' corresponds to modifying the weightage factor
to . In this paper, we use this modified
weightage factor in Schwinger's proper time formalism to evaluate the quantum
gravitational corrections to some of the standard quantum field theoretic
results in flat and curved spacetimes. We find that the extra factor
acts as a regulator at the Planck scale thereby `removing' the
divergences that otherwise appear in the theory. Finally, we discuss the wider
implications of our analysis.Comment: 26 pages, Revte
Event horizon - Magnifying glass for Planck length physics
An attempt is made to describe the `thermodynamics' of semiclassical
spacetime without specifying the detailed `molecular structure' of the quantum
spacetime, using the known properties of blackholes. I give detailed arguments,
essentially based on the behaviour of quantum systems near the event horizon,
which suggest that event horizon acts as a magnifying glass to probe Planck
length physics even in those contexts in which the spacetime curvature is
arbitrarily low. The quantum state describing a blackhole, in any microscopic
description of spacetime, has to possess certain universal form of density of
states which can be ascertained from general considerations. Since a blackhole
can be formed from the collapse of any physical system with a low energy
Hamiltonian H, it is suggested that when such a system collapses to form a
blackhole, it should be described by a modified Hamiltonian of the form
where .I also show
that it is possible to construct several physical systems which have the
blackhole density of states and hence will be indistinguishable from a
blackhole as far as thermodynamic interactions are concerned. In particular,
blackholes can be thought of as one-particle excitations of a class of {\it
nonlocal} field theories with the thermodynamics of blackholes arising
essentially from the asymptotic form of the dispersion relation satisfied by
these excitations. These field theoretic models have correlation functions with
a universal short distance behaviour, which translates into the generic
behaviour of semiclassical blackholes. Several implications of this paradigm
are discussed
Response of finite-time particle detectors in non-inertial frames and curved spacetime
The response of the Unruh-DeWitt type monopole detectors which were coupled
to the quantum field only for a finite proper time interval is studied for
inertial and accelerated trajectories, in the Minkowski vacuum in (3+1)
dimensions. Such a detector will respond even while on an inertial trajctory
due to the transient effects. Further the response will also depend on the
manner in which the detector is switched on and off. We consider the response
in the case of smooth as well as abrupt switching of the detector. The former
case is achieved with the aid of smooth window functions whose width, ,
determines the effective time scale for which the detector is coupled to the
field. We obtain a general formula for the response of the detector when a
window function is specified, and work out the response in detail for the case
of gaussian and exponential window functions. A detailed discussion of both and limits are given and several
subtlities in the limiting procedure are clarified. The analysis is extended
for detector responses in Schwarzschild and de-Sitter spacetimes in (1+1)
dimensions.Comment: 29 pages, normal TeX, figures appended as postscript file, IUCAA
Preprint # 23/9
Observational constraints on low redshift evolution of dark energy: How consistent are different observations?
The dark energy component of the universe is often interpreted either in
terms of a cosmological constant or as a scalar field. A generic feature of the
scalar field models is that the equation of state parameter w= P/rho for the
dark energy need not satisfy w=-1 and, in general, it can be a function of
time. Using the Markov chain Monte Carlo method we perform a critical analysis
of the cosmological parameter space, allowing for a varying w. We use
constraints on w(z) from the observations of high redshift supernovae (SN), the
WMAP observations of CMB anisotropies and abundance of rich clusters of
galaxies. For models with a constant w, the LCDM model is allowed with a
probability of about 6% by the SN observations while it is allowed with a
probability of 98.9% by WMAP observations. The LCDM model is allowed even
within the context of models with variable w: WMAP observations allow it with a
probability of 99.1% whereas SN data allows it with 23% probability. The SN
data, on its own, favors phantom like equation of state (w<-1) and high values
for Omega_NR. It does not distinguish between constant w (with w<-1) models and
those with varying w(z) in a statistically significant manner. The SN data
allows a very wide range for variation of dark energy density, e.g., a
variation by factor ten in the dark energy density between z=0 and z=1 is
allowed at 95% confidence level. WMAP observations provide a better constraint
and the corresponding allowed variation is less than a factor of three.
Allowing for variation in w has an impact on the values for other cosmological
parameters in that the allowed range often becomes larger. (Abridged)Comment: 21 pages, PRD format (Revtex 4), postscript figures. minor
corrections to improve clarity; references, acknowledgement adde
Dark Energy and Gravity
I review the problem of dark energy focusing on the cosmological constant as
the candidate and discuss its implications for the nature of gravity. Part 1
briefly overviews the currently popular `concordance cosmology' and summarises
the evidence for dark energy. It also provides the observational and
theoretical arguments in favour of the cosmological constant as the candidate
and emphasises why no other approach really solves the conceptual problems
usually attributed to the cosmological constant. Part 2 describes some of the
approaches to understand the nature of the cosmological constant and attempts
to extract the key ingredients which must be present in any viable solution. I
argue that (i)the cosmological constant problem cannot be satisfactorily solved
until gravitational action is made invariant under the shift of the matter
lagrangian by a constant and (ii) this cannot happen if the metric is the
dynamical variable. Hence the cosmological constant problem essentially has to
do with our (mis)understanding of the nature of gravity. Part 3 discusses an
alternative perspective on gravity in which the action is explicitly invariant
under the above transformation. Extremizing this action leads to an equation
determining the background geometry which gives Einstein's theory at the lowest
order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy,
edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure
Initial state of matter fields and trans-Planckian physics: Can CMB observations disentangle the two?
The standard, scale-invariant, inflationary perturbation spectrum will be
modified if the effects of trans-Planckian physics are incorporated into the
dynamics of the matter field in a phenomenological manner, say, by the
modification of the dispersion relation. The spectrum also changes if we retain
the standard dynamics but modify the initial quantum state of the matter field.
We show that, given {\it any} spectrum of perturbations, it is possible to
choose a class of initial quantum states which can exactly reproduce this
spectrum with the standard dynamics. We provide an explicit construction of the
quantum state which will produce the given spectrum. We find that the various
modified spectra that have been recently obtained from `trans-Planckian
considerations' can be constructed from suitable squeezed states above the
Bunch-Davies vacuum in the standard theory. Hence, the CMB observations can, at
most, be useful in determining the initial state of the matter field in the
standard theory, but it can {\it not} help us to discriminate between the
various Planck scale models of matter fields. We study the problem in the
Schrodinger picture, clarify various conceptual issues and determine the
criterion for negligible back reaction due to modified initial conditions.Comment: revtex4; 17 page
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